Single-pixel imaging (SPI) enables an invisible target to be imaged onto a photosensitive surface without a lens, emerging as a promising way for indirect optical encryption. However, due to its linear and broadcast imaging principles, SPI encryption has been confined to a single-user framework for the long term. We propose a multi-image SPI encryption method and combine it with orthogonal frequency division multiplexing-assisted key management, to achieve a multiuser SPI encryption and authentication framework. Multiple images are first encrypted as a composite intensity sequence containing the plaintexts and authentication information, simultaneously generating different sets of keys for users. Then, the SPI keys for encryption and authentication are asymmetrically isolated into independent frequency carriers and encapsulated into a Malus metasurface, so as to establish an individually private and content-independent channel for each user. Users can receive different plaintexts privately and verify the authenticity, eliminating the broadcast transparency of SPI encryption. The improved linear security is also verified by simulating attacks. By the combination of direct key management and indirect image encryption, our work achieves the encryption and authentication functionality under a multiuser computational imaging framework, facilitating its application in optical communication, imaging, and security.
Phase Measuring Deflectometry (PMD) with high dynamic range and high robustness is a more powerful method to achieve the integration of optical components fabrication and testing, which would avoid the secondary positioning error caused by the removal of optical components in off-line status. However, for surface shape measurement of transparent element, the captured fringe patterns are superposition of the patterns reflected from the front and rear surfaces, leading to the failure of the traditional phase-shifting algorithm to extract the true phase distribution. In order to separate the superposed fringe patterns, the limitations of the existing methods such as UV deflectometry and polarized light deflectometry, which require special light source and polarizer filter, are expensive instrument and complex processes. Moreover, only the front surface shape can be reconstructed at a time, which lowers the efficiency of the measurement. To achieve in-situ measurement of the front and rear surface shapes of the transparent element simultaneously, the combination of PMD and power spectrum estimation is used to separate parasitic fringe patterns. And the front and rear surface shapes are reconstructed using ray tracing and non-linear optimization. The feasibility of the proposed method is demonstrated by numerical simulation. In the experiment, the transparent element with a thickness of about 10 mm is detected and the front and rear surface shapes are reconstructed. The front and rear surface shapes differences of the transparent element with a diameter of 77.8 mm are 173 nm in RMS and 212 nm in RMS, respectively.
Digital image correlation (DIC) is a widely used non-contact measurement method for the deformation of a diffused object surfaces in the experimental solid mechanics. In specular surface figure measurement, the rapidly developing deflectometry using sinusoidal fringes can achieve a sub-micron level accuracy. The fringe pattern used in the phase shift algorithm is sensitive to noise, but the speckle image used in the DIC technique is robust against noise. In this paper, three kinds of speckle deflectometry methods, which are speckle pattern defletometry(SPD), speckle pattern shifting deflectometry(SPSD) and dynamic speckle deflectometry(DSD), are introduced to measure the figure of specular surface. The principles of the three methods are introduced in detail, and the experimental results are given in order to illustrate the measurement accuracy.
In traditional phase measurement deflectometry (PMD), a number of sinusoidal fringe patterns are displayed on the screen in two orthogonal directions, which is time-consuming and not suitable for dynamic measurements. A phase-extraction algorithm based on the spatial-carrier phase-shifting technology for a single-shot spatial-carrier orthogonal fringe pattern is proposed. The phase increment of each pixel in two orthogonal directions is obtained by the least squares method and then the amount of spatial phase shift of all pixels relative to the probe pixel in the rectangular neighborhood centered on the probe pixel can be obtained. The number of fringe patterns required for the PMD is reduced to one by displaying a spatial-carrier orthogonal fringe pattern. Finally, the feasibility of the algorithm is verified by simulation and experiment.
For on-line surface measurement of transparent optical elements, phase measuring deflectometry (PMD) is a very promising method. However, the parasitic reflection from the rear surface is an existing problem for PMD to measure transparent element. A parasitic reflection eliminating method using binary pattern is proposed, the principle of which is described in detail. And the proposed method is implemented on a transparent window glass with a thickness of about 10mm. The surface shape result shows a good agreement with the interferometer data with a sub-wavelength level accuracy.
In the phase measurement deflectometry, sinusoidal fringe patterns are separately projected on a specular test surface, and the distorted fringes reflected by the surface are recorded by a charge-coupled device (CCD) camera. The phase shift algorithm is used to find the position of the light source on the display corresponding to the pixel point on the CCD, thereby calculating the slope of each point on the element to be tested, and finally retrieving the surface shape of the test element by using the surface reconstruction algorithm. The phase information is usually obtained by traditional 16-step phase-shifting algorithm, which involves certain complicated and time-consuming procedures, for instance, fringe projection in the horizontal and vertical directions. Therefore, to avoid these procedures, a four-step phase shift algorithm based on crossed fringes is proposed. Based on Gram–Schmidt orthonormalization method, only four crossed fringe patterns are needed to determine the phase in both directions simultaneously. Both numerical simulation and experiment are conducted to verify the validity of the algorithm.
Phase measuring deflectometry (PMD) with structured light projection and phase-shifting technique is a highly accurate optical surface measuring method. For surface shape measurement of transparent planar elements, PMD suffers from parasitic reflection. To avoid the unwanted effect of parasitic reflection, a method based on fringe frequency tuning and Fourier-transform is introduced in this paper. Numerical simulations and experiments are both conducted to evaluate the performance of the proposed method. An optical planar element with a thickness of 24.5mm is measured, and measurement error is within 200nm PV.
Phase measuring deflectometry (PMD) with structured light projection and phase-shifting technique is a highly accurate optical surface measuring method based on the law of reflection. Generally, for surface shape measurement of transparent planar elements, PMD suffers from parasitic reflection. To avoid the unexpected effect of parasitic reflection, a method based on fringe frequency tuning and Fourier-transform is introduced. Numerical simulations and experiments are both conducted to evaluate the performance of the proposed method. Experiment results are shown. Surface figures measured using the proposed method are compared with those measured using traditional phase-shifting algorithm and Fizeau interferometer. Both an optical planar element with a thickness of 24.5 mm and a planar window glass with a thickness of 10 mm are measured. For the optical element, the proposed method is accurate and the measurement error is within 200-nm PV. For window glass, the proposed method yields a better surface figure than the traditional phase-shifting algorithm does.
Absolute measurement with Phase Measuring Deflectometry (PMD) is gaining importance in industry, but the accuracy of deflectometry metrology is strongly influenced by the level of calibration. In order to improve the accuracy of the PMD to a level where it competes with interferometry, a reference calibration process is commonly carried out to carefully calibrate the systematic errors. The systematic errors obtained by measuring a high quality reference surface can be subtracted from the measurement of a test surface to get its actual surface, however, it could introduce the surface error of reference into the measurement. To alleviate this problem, this paper introduces a technique named “rotational shear phase measuring deflectometry”, this technique have the ability of removing the rotationally asymmetric systematic errors from the test surface without using a reference surface. The validity of this technique has been demonstrated by simulation and our experimental results.
In phase measuring deflectometry, two orthogonal sinusoidal fringe patterns are separately projected on the test surface and the distorted fringes reflected by the surface are recorded, each with a sequential phase shift. Then the two components of the local surface gradients are obtained by triangulation. It usually involves some complicated and time-consuming procedures (fringe projection in the orthogonal directions, accurate phase shifting).To avoid the complex process, a novel phase extraction algorithm with crossed fringes is presented in this paper. It is based on a least-squares iterative process. Both a numerical simulation and a preliminary experiment are conducted to verify the validity and performance of this algorithm. Experimental results obtained by our method are shown, and comparisons between our experimental results and those obtained by the traditional phase-shifting algorithm and between our experimental results and those measured by the Fizeau interferometer are made.
Common problems faced in optical comprehensive design experiment and going against the Washington Accord are pointed out. For resolving these problems, an instructional and innovative teaching scheme for Optics Comprehensive Design Experiment is proposed. We would like to understand the student that can improve the hands-on practical ability, theory knowledge understanding ability, complex problem solving ability, engineering application ability, cooperative ability after tracking and researching the student who have attended the class about Optical Comprehensive Design Experiment, We found that there are some problems on the course such as the experiment content vague, the student beginning less time, phase separation theory and engineering application, the experiment content lack of selectivity and so on. So we have made some improvements reference to the Washington Accord for the class teaching plan about Optical Comprehensive Design Experiment. This class must relevant to the engineering basic courses, professional foundation course and the major courses, so far as to the future study and work that which can play a role in inheriting and continuity to the students. The Optical Comprehensive Design Experiment teaching program requires students learning this course to have learnt basic courses like analog electronics technique, digital electronic technique, applied optics and computer and other related courses which students are required to comprehensively utilize. This teaching scheme contains six practical complex engineering problems which are respectively optical system design, light energy meter design, illuminometer design, material refractive index measuring system design, light intensity measuring system design and open design. Establishing the optional experiment and open experiment can provide students with a greater choice and enhance the students' creativity, vivid teaching experimental teachers and enriching contents of experiment can make the experiment more interesting, providing students with more opportunities to conduct experiment and improving students' practical ability with long learning time, putting emphasis on student's understanding of complex engineering problems and the cognitive of the process to solve complex engineering problems with actual engineering problems. Applying the scheme in other courses and improving accordingly will be able to ensure the quality of engineering education. Look forward to offering useful reference for the curriculum system construction in colleges and universities.
Phase Measuring Deflectometry(PMD) is a non-contact, high dynamic-range and full-field metrology which becomes a serious competitor to interferometry. However, the accuracy of deflectometry metrology is strongly influenced by the level of the calibrations. Our paper presents a calibration-based PMD method to test optical flat surface with a high accuracy. In our method, a pin-hole camera was set next to the LCD screen which is used to project sinusoidal fringes to the test flat. And the test flat was placed parallel to the direction of the LCD screen, which makes the geometry calibration process are simplified. The photogrammetric methods used in computer vision science was used to calibrate the pin-hole camera by using a checker pattern shown on another LCD display at six different orientations, the intrinsic parameters can be obtained by processing the obtained image of checker patterns. Further, by making the last orientation of checker pattern is aligned at the same position as the test optical flat, the algorithms used in this paper can obtain the mapping relationship between the CCD pixels and the subaperture coordinates on the test optical flat. We test a optical flat with a size of 50mm in diameter using our setup and algorithm. Our experimental results of optical flat figure from low to high order aberrations show a good agreement with that from the Fizeau interferometer.
A new wavefront reconstruction algorithm for radial shearing interferometer is proposed. Based on the shearing relationship between the expanded wavefront and the test wavefront, the interpolation coefficient matrix are established by the radial shearing ratio and the number of discrete points of test wavefront. Accordingly, the expanded wavefront can be described by an interpolation coefficient matrix and the test wavefront. Then the test wavefront can be calculated from the phase difference wavefront which comes from any radial shearing interferometer. The numerical simulation proves the correctness of the algorithm. The main error source of this algorithm has been analyzed and the error propagation coefficient has been calculated at last. Above results show that the proposed algorithm is an effective and correct algorithm to reconstruct wavefront for radial shearing interferometer.
Zonal wavefront reconstruction by use of the well known Southwell algorithm with rectangular grid patterns has been considered in the literature. However, when the grid patterns are nonrectangular, modal wavefront reconstruction has been extensively used. We propose an improved zonal wavefront reconstruction algorithm for Hartmann type test with arbitrary grid patterns. We develop the mathematical expressions to show that the wavefront over arbitrary grid patterns, such as misaligned, partly obscured, and non-square mesh grids, can be estimated well. Both iterative solution and least-square solution for the proposed algorithm are described and compared. Numerical calculation shows that the zonal wavefront reconstruction over nonrectangular profile with the proposed algorithm results in a significant improvement in comparison with the Southwell algorithm.
Self-referencing interferometry has been widely used in wavefront sensing. However, currently the results of wavefront measurement include two parts, one is the real phase information of wavefront under test and the other is the system error in self-referencing interferometer. In this paper, a method based on maximum likelihood estimation is presented to calibrate the system error in self-referencing interferometer. Firstly, at least three phase difference distributions are obtained by three position measurements of the tested component: one basic position, one rotation and one lateral translation. Then, combining the three phase difference data and using the maximum likelihood method to create a maximum likelihood function, reconstructing the wavefront under test and the system errors by least square estimation and Zernike polynomials. The simulation results show that the proposed method can deal with the issue of calibration of a self-referencing interferometer. The method can be used to reduce the effect of system errors on extracting and reconstructing the wavefront under test, and improve the measurement accuracy of the self-referencing interferometer.
A color holographic display method is proposed. It uses a spatial light modulator with a synthetic computer-generated hologram, which includes red, green, and blue three monochromatic scenes’ information. We calculate three holograms corresponding to red, green, and blue, and then generate a color hologram according to the law of sampling. A filter owning the pixel structure is designed so that white light emitting diode can be used as reconstructed light. We numerically evaluate the image quality of color-reconstructed images and compare the quality of color-reconstructed images with that of reconstructed color images using another color holographic projection method. The experimental results verify the feasibility of the method.
We propose an integral imaging in which the micro-lens array in the pickup process called MLA 1 and the micro-lens array in the display process called MLA 2 have different specifications. The elemental image array called EIA 1 is captured through MLA 1 in the pickup process. We deduce a pixel mapping algorithm including virtual display and virtual pickup processes to generate the elemental image array called EIA 2 which is picked up by MLA 2. The 3D images reconstructed by EIA 2 and MLA 2 don’t suffer any image scaling and distortions. The experimental results demonstrate the correctness of our theoretical analysis.
We propose an integral imaging in which the micro-lens array (MLA) in the pickup process called MLA 1 and the micro-lens array in the display process called MLA 2 have different specifications. The elemental image array called EIA 1 is captured through MLA 1 in the pickup process. We deduce a pixel mapping algorithm including virtual display and virtual pickup processes to generate the elemental image array called EIA 2 which is picked up by MLA 2. The three-dimensional images reconstructed by EIA 2 and MLA 2 do not suffer any image scaling and distortions. The experimental results demonstrate the correctness of our theoretical analysis.
KEYWORDS: Integral imaging, 3D displays, 3D image processing, Communication engineering, Autostereoscopic displays, Lenticular lenses, Lithium, Image resolution, Modulation, Optical engineering
We analyze the effect of aperture width of the parallax barrier on the viewing angle of one-dimensional integral imaging (1-DII) display and propose a 1-DII display that consists of a display panel and a variable parallax barrier. When the variable parallax barrier changes its aperture width, the viewing angle and the optical efficiency of the proposed 1-DII display are compared. The viewing angle is increased by decreasing the aperture width of the variable parallax barrier, while the optical efficiency is increased by increasing the aperture width of the variable parallax barrier.
An integral imaging (II) display is proposed which consists of a display panel and a gradient-aperture pinhole array. The gradient-aperture pinhole array is symmetrical in both horizontal and vertical directions. The leftmost and rightmost pinholes are used to fix the horizontal viewing angle, and the uppermost and nethermost pinholes are used to fix the vertical viewing angle. To increase the optical efficiency, the aperture widths of other pinholes are gradually increased from both sides to the middle in the horizontal and vertical directions, respectively. A prototype of the proposed II display is developed. Its horizontal viewing angle is equal to that of the conventional one, while its optical efficiency is higher than that of the conventional one.
Optical metrology for elements with large dynamic range is very important, especially in aspheric components testing
field. Cyclic radial shearing interferometer(CRSI) with a small radial shearing ratio of the expanded wavefront's radii to
the contracted version's radii can obtain a small magnitude optical path difference(OPD) because the expanded
wavefront and its contracted version nearly have the same shape and magnitude, especially for an optical component to
be tested with rotationally symmetric surface. The number of fringe pattern can be decreased dramatically and recorded
by CCD. This paper demonstrates the feasibility that CRSI could be used to measure an aspheric surface with large
dynamic range and large aperture.
When a fiber with four layers is illuminated by a laser beam collimated perpendicular to its axis, an asymmetry in the frontscattered light pattern will be observed. In our opinions, the eccentricity of fiber core results in it. We deduced the formula and achieved the intensity display from the different path between refracted rays by whole four layers and reflected rays by the fiber core using geometric ray tracing, and calculated the interference geometrically between the refracted rays that traverse whole four layers and one that go through only the outside three layers. The latter is responsible for the modulation of the intensity display. We found that the theoretical values nearly agreed with the experiment and the 5% eccentricity of the fiber core can be inspected. At the same time, this method can be used to in- line inspection of the eccentricity for the fiber manufacturing.
A simple phase-shift interference methods using a couple of double slits and a cylindrical lens are proposed to measure the phase modulation characteristics of liquid crystal spatial light modulator (LC-SLM). The experimental results employed the proposed in this paper are presented.
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